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Finite‐difference time‐domain simulation of acoustic propagation in heterogeneous dispersive medium
Author(s) -
Norton Guy V.
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20231
Subject(s) - mathematics , mathematical analysis , acoustic wave equation , convolution (computer science) , acoustics , scattering , time derivative , time domain , acoustic wave , wave propagation , partial differential equation , finite difference time domain method , nonlinear acoustics , finite difference , nonlinear system , finite difference method , physics , optics , computer science , artificial neural network , quantum mechanics , machine learning , computer vision
Accurate modeling of pulse propagation and scattering is a problem in many disciplines (i.e., electromagnetics and acoustics). It is even more tenuous when the medium is dispersive. Blackstock [D. T. Blackstock, J Acoust Soc Am 77 (1985) 2050] first proposed a theory that resulted in adding an additional term (the derivative of the convolution between the causal time‐domain propagation factor and the acoustic pressure) that takes into account the dispersive nature of the medium. Thus deriving a modified wave equation applicable to either linear or nonlinear propagation. For the case of an acoustic wave propagating in a two‐dimensional heterogeneous dispersive medium, a finite‐difference time‐domain representation of the modified linear wave equation can been used to solve for the acoustic pressure. The method is applied to the case of scattering from and propagating through a 2‐D infinitely long cylinder with the properties of fat tissue encapsulating a cyst. It is found that ignoring the heterogeneity in the medium can lead to significant error in the propagated/scattered field. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007